How do you find the value of the discriminant and determine the nature of the roots 5b^2+b-2=0?

Jun 1, 2017

The discriminant is $41$ and therefore there are 2 distinct real-number solutions.

Explanation:

If a quadratic equation is in the form:

$a {x}^{2} + b x + c$

The discriminant is defined to be:

${b}^{2} - 4 a c$

${1}^{2} - 4 \left(5\right) \left(- 2\right)$

$1 + 40 = 41$

Since the discriminant is positive, there are 2 distinct real-number solutions.

If the discriminant is negative, there are no real-number solutions and if the discriminant is $0$, one repeated real-number solution.